The frog jumped approximately 16.18 feet horizontally. The maximum height it jumped was approximately 4.65 feet.
Explanation:The function y = -0.017x^2 + 0.55x models the frog's jump, it represents a parabola where the highest point, the vertex, means the highest point the frog reached, and where it hits the x-axis indicates the horizontal distance the frog jumped. We can find the distance of the frog's jump by setting y to 0 and solving the equation for x, whereas, the maximum height of the frog's jump will be determined by the vertex of the parabola.
For a function in the form y = ax^2 + bx + c, the x-value of the vertex, which is the maximum height in this context, can be found by using the formula -b/2a.
Substituting the given values from the equation, -b/2a = -0.55/(-2*-0.017) = 16.18 feet approximately.
Substitute x = 16.18 feet into the given function to find the maximum height the frog jumped: y = -0.017*(16.18)^2 + 0.55*16.18 = 4.65 feet approximately.
So, the frog jumped approximately 16.18 feet horizontally and the maximum height it jumped was approximately 4.65 feet.
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The frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet. We found this by setting the quadratic function to zero and solving for the horizontal distance, and by calculating the vertex of the parabola for the maximum height of the jump.
The function y = -0.017x^2 + 0.55x models the height y, in feet, of your pet frog's jump, where x is the horizontal distance, in feet, from the start of the jump. To determine how far the frog jumped, we look for the value of x when y equals zero, which represents when the frog lands back on the ground. To find this, we set the equation equal to zero and solve for x:
0 = -0.017x^2 + 0.55x
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = -0.017, b = 0.55, and c = 0. We can solve this by factoring or using the quadratic formula. The solutions to this equation represent the starting point (x=0) and the landing point of the jump. Ignoring the x=0 solution, we find that the frog lands at approximately x = 32.35 feet (after rounding to the nearest hundredth).
To determine how high the frog went, we need to find the vertex of the parabola because this represents the highest point of the jump. The x-coordinate of the vertex is given by -b/(2a), so we calculate:
x = -0.55 / (2 * -0.017) = 16.18 (rounded to the nearest hundredth)
We plug this value into the original equation to find the height:
y = -0.017(16.18)^2 + 0.55(16.18) = approximately 4.71 feet (after rounding to the nearest hundredth)
Therefore, the frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet.
How to factor with a number in front of the first variable?
The sum of two numbers is 56. Their difference is 18.
The numbers are 37 and 19
From the question,
Let the numbers be x and y
From the first statement
The sum of two numbers is 56.
That is,
x + y = 56 --------- (1)
From the second statement
Their difference is 18
That is,
x - y = 18 ----------- (2)
Add equations (1) and (2)
x + y + x - y = 56 + 18
2x = 74
∴ x = 74 ÷ 2
x = 37
Substitute the value of x into equation (1) to determine the value of y
x + y = 56
37 + y = 56
y = 56 - 37
y = 19
∴ x = 37 and y = 19
Hence, the numbers are 37 and 19.
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How to solve systems of linear equations step by step?
Plz help! 2 questions!! A machine is wrapping 18 boxes in 5 minutes. If the machine continues at the same rate, how many boxes will it rap in 25 minutes ? A.38 B.90 C.23 D.72
Chris is making lemonade. The directions say to mix 5 cups of water with 2 scoops of powdered lemonade mix. How many cups of water should he use with 2.5 scoops of fruit mix? A.6 B.6.25 C.6.5 D. 6.75
find the slope of a line whose equation is 3X+6Y=9
To find the slope of the above equation, it is easiest to put it into slope-intercept form, y=mx + b, where the variable m represents the slope. To do this, we must isolate the variable y on the left side of the equation by using the reverse order of operations. First, we should subtract 3x from both sides of the equation.
3x + 6y = 9
6y = -3x + 9
Next, we should divide both sides of the equation by 6 to undo the coefficent of 6 on the variable y.
y = -1/2x + 3/2
Therefore, the slope of the line is -1/2 (the coefficient of the variable x in slope-intercept form).
Hope this helps!
Sondra lives in Nebraska and pays 5.5% in sales tax. If she just bought a belt that cost $22, what was the total amount she paid for the belt, including sales tax?
A.$12.10
B.$20.79
C.$34.10
D.$23.21
please help
5.5% = 0.055
22 * 0.055 = 1.21
22 + 1.21 = 23.21
Answer is D
Answer:
D. $23.21
Step-by-step explanation:
We have been given that Sondra lives in Nebraska and pays 5.5% in sales tax. She just bought a belt that cost $22.
The total amount paid by Sondra for the belt will be equal to cost of belt plus 5.55 of the cost of the belt.
[tex]\text{Total amount paid by Sondra}=\$22+(\frac{5.5}{100}\times \$22)[/tex]
[tex]\text{Total amount paid by Sondra}=\$22+(0.055\times \$22)[/tex]
[tex]\text{Total amount paid by Sondra}=\$22+\$1.21[/tex]
[tex]\text{Total amount paid by Sondra}=\$23.21[/tex]
Therefore, the total amount paid Sondra for belt is $23.21 and option D is the correct choice.
Which statement is true about the graphs of the two lines y = x + 2 and y = x ?
The lines are perpendicular to each other because and are opposite reciprocals of each other.
The lines are perpendicular to each other because 2 and are opposite reciprocals of each other.
The lines are neither parallel nor perpendicular to each other because and are not opposite reciprocals of each other.
The lines are neither parallel nor perpendicular to each other because 2 and are not opposite reciprocals of each other.
How has the Customer Service Institute of America helped the banking industry?
A by creating a centralized call center to handle all banking complaints
B by setting standards that help banks measure their level of customer service
C by creating customer service surveys for banks
D by implementing a program for bank executives
Answer:
by setting standards that help banks measure their level of customer service
Step-by-step explanation:
What is the definition of principal square root in math?
Final answer:
The principal square root in math refers to the positive square root of a number. It is denoted as √x and is applicable to non-negative numbers.
Explanation:
The principal square root in math refers to the positive square root of a number. It is denoted as √x, where x is a non-negative number.
For example, the principal square root of 25 is √25 = 5 because 5 multiplied by itself equals 25.
The principal square root is only applicable to non-negative numbers, while negative numbers have no real square roots.
How can you describe the solution set of the equation 16x2 - 8x + 1 = 0?
1. Which ordered pairs are a solution to the equation?
y = 3x - 4
options:
(4,2)
(1, -1)
(-1, -7)
(2, 2)
2.Which ordered pairs are a solution to the equation?
y = 4 - 2x
options:
(-1,2)
(0,4)
(-1,6)
(1,6)
Choose the expression that would equal the number of hours in the following question.
If a car averages 50 1/2 miles per hour, how many hours will it take to go 47 1/2 miles?
A: 583/6
B: 285/302
C: 302/285
D: 45,602/6
Diane left a 15% tip for a meal that cost $44.
What was the amount of the tip?
Answer:
6.60
Step-by-step explanation:
which value for the number makes the statement true?
the quotient of a number and five is eight
a.4
b.8
c.40
d.80
Which of the following points lie in the solution set to the following system of inequalities?
y > −3x + 3
y > x + 2
choices:
(2, −5)
(−2, 5)
(2, 5)
(−2, −5)
Which equation shows how the properties of numbers extend to negative whole numbers by the Commutative Property of Addition?
A) −2 + 4 = 4 + (−2)
B) −2(4) = 4(−2)
C) (−2 + 4) + 3 = −2 + (4 + 3)
D) −2(4 + 3) = (−2 x 4) + (−2 x 3)
Answer:
Your answer is gonna be D
PLEASE HELP QUICK I'M OFFERING BRAINLIEST ANSWER & 10PTS
What is the total flow (loads per week) between department y and department z?
A company needs to locate three departments (X, Y, and Z) in
the three areas (I, II, and III) of a new facility. They want to minimize
interdepartmental transportation costs, which are expected to be $.50 per load
per meter moved. An analyst has prepared the following distances and flow
matrices:
Distances (meters):
From/TO I II III
I - 10 20
II - 10
III -
Flows (loads per week:
From/TO I II III
X - 60 90
Y 40 - 160
Z 110 140 -
What is the total flow (loads per week) between department Y
and department Z?
E. 300
Find the quotient.
22x ^2 y ^2 ÷ 11x ^2 y ^2
0
1/2
2
2xy
Solve the inequality.
q + 12 – 2(q – 22) > 0
q < 56
q > –32
q > 56
q < –32
Answer:
q<56
Step-by-step explanation:
An inequality is an algebraic expression that consists of two members separated by an inequality. The inequality can be <, ≤,>, ≥.
Solving an inequality consists in finding the value or values that verify it.
An inequality of the first degree is an inequality in which the variable is of degree one, as in this particular case.
In this case, the resolution must first eliminate the parentheses on the left side of the inequality. For that you apply distributive property. This property expresses that the multiplication of a number by a sum is equal to the sum of the multiplications of that number by each of the addends. So you get:
q+12-2*q-2*(-22)>0
q+12-2*q+44>0
Then the terms contained in "q" must be grouped on one side of the inequality and the independent terms on the other. In this case the terms with the variable "q" will remain on the left side of the inequality. The independent terms will be grouped on the right side, remembering that to take them to the other side of the inequality the opposite operations will be used. This is:
the opposite operation of the sum is the subtraction .the opposite operation of subtraction is the sum .the opposite operation of multiplication is division .the opposite operation of the division is multiplication.So:
q-2q>-12-44
Solving the corresponding addition and subtraction operations you get:
(-1)*q>-56
Since the coefficient that accompanies "q" is negative, it is multiplied by −1 on both sides of the inequality, so the direction of inequality will change.
q<56
Finally, the values for which the inequality is valid are those in which q is less than 56
In one study, the correlation coefficient of measured iq at ages 8 and 10 was .88. this shows a _____ correlation.
Express the area of a rectangle as a function of the width w if the width of the rectangle is twice its length
plz plz plz help!!!!!
The Griffins and the Corbins live in the same city and pay the same sales tax rate, and both families made $12,000 in taxable purchases last year. If the Griffins made $73,000 and the Corbins made $29,000 last year, is the sales tax in their city an example of a regressive tax?
A.Yes, because the Corbins paid a higher percentage of their income in sales tax than the Griffins did.
B.No, because the Corbins paid a higher percentage of their income in sales tax than the Griffins did.
C.No, because the Griffins and the Corbins both paid the same sales tax rate.
D.Yes, because the Griffins and the Corbins both paid the same sales tax rate.
Answer:
The correct answer is A.
Step-by-step explanation:
A.Yes, because the Corbins paid a higher percentage of their income in sales tax than the Griffins did.
Regressive tax is applied uniformly and this causes lower-income people to pay a larger share of their income than rich people. It is not a fair way though it seems to be. Most regressive taxes are not income taxes.
Can someone please clearly explain and workout Q5? Much appreciated
A color printer prints 24 pages in 7 minutes. how many pages does it print per minute?
Final answer:
The color printer prints approximately 3.43 pages per minute. This is calculated by dividing the total number of pages (24) by the total printing time in minutes (7).
Explanation:
To calculate the number of pages a color printer prints per minute, we use the information provided that it prints 24 pages in 7 minutes. The calculation is a simple division problem:
Determine the rate by dividing the total number of pages by the total number of minutes.Pages per minute = Total pages printed ÷ Total minutesPages per minute = 24 pages ÷ 7 minutesCalculate the quotient to find the page rate.Pages per minute ≈ 3.43 pages per minuteTherefore, the printer prints approximately 3.43 pages per minute.
What is the length of BC¯¯¯¯¯ ?
Enter your answer in the box.
Answer: The required length of BC is 22 units.
Step-by-step explanation: We are given to find the length of BC from the figure.
From the figure, we note that ABC is an isosceles triangle, with AC = AB, where
AC = 2x-24, AB = x-2 and BC = x.
Since AC = AB, so we get
[tex]2x-24=x-2\\\\\Rightarrow 2x-x=24-2\\\\\Rightarrow x=22.[/tex]
Therefore, we get
BC = x = 22.
Thus, the required length of BC is 22 units.
A student received an 82% on an exam. If there were 50 questions on the exam, which ratio would show the number of questions answered correctly? A. 82:50 B. 25:50 C. 59:50 D. 41:50
How do you solve 18b2c-12ab3+30ab?
Assume that we want to find the probability that when five consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Also assume that 38% of consumers are comfortable with the drones (based on a survey). Identify the values of n, x, p, and q. The value of n is __. (Type an integer or a decimal. Do not round.) The value of x is __. (Type an integer or a decimal. Do not round.) The value of p is __. (Type an integer or a decimal. Do not round.) The value of q is ___ . (Type an integer or a decimal. Do not round.)
In the given problem, n (the number of trials) is 5, x (the amount of 'successes' we're seeking) is 2, p (the probability of success) is 0.38, and q (the probability of failure) is 0.62.
Explanation:In the given problem, we are conducting a binomial experiment where five consumers are randomly selected and we are interested in the number who are comfortable with drone delivery. So, the total number of trials, n, will be equal to the number of consumers selected, which is 5.
The value to be observed, x, is exactly 2, because we want to find out the probability of exactly two of them are comfortable with delivery by drones.
The probability of success, p, is the proportion of consumers that are comfortable with delivery by drones, so p = 0.38 (or 38%).
The probability of failure, q, is the proportion of consumers that are not comfortable with delivery by drones, so q = 1 - p = 1 - 0.38 = 0.62.
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